Markup is the process of transferring a pattern and its dimensions to a workpiece. Marking is of great importance for the individual production of jewelry. Proper, well-executed, it greatly facilitates the high-quality production of jewelry. In most cases, jewelry marking is used to place small stones on the “top” of the product, as well as to transfer the pattern for subsequent sawing or cutting. Marking is carried out on small sheet metal, which creates its own difficulties.
Marking tools are scribers, compasses, scale ruler (metal), center punches. The marking of small plates is carried out on marking plates (sheets).
The scriber is a rod with a pointed end. The working end of the scriber must be made of steel, hardened and have a sharpening angle of not more than 20 °. The scriber rod itself can be made of any material (aluminum, plastic, wood). The length and diameter of the rod are taken equal to the pencil. There are scribers with a collet clamp for a working needle. The scriber is used for drawing marks on the surface to be marked both by ruler, square, template, and by hand.
The marking compass (Fig. 29) for fine marking is made of steel. To separate the legs of the compass in the middle part there is a locking screw that fixes the distance between the legs. The non-working ends of the legs are connected by a spring ring to keep the legs in constant tension. The compasses must be rigid, in working condition, have no backlash vibrations. The height of the compass is 75-100 mm, the maximum dilution of the legs is 50-80 mm, respectively. The working ends of the compass are sharpened so as to form a cutting angle. A marking compass is used to transfer linear dimensions from a scale ruler to a workpiece, to divide lines into the desired segments, construct angles, draw circles and arcs, and divide a circle into the required number of axes.

The scale ruler should be metal, 100 - 150 mm long, with a smooth working edge without notches and a clear dividing scale. The ruler is used for making straight marks with a scriber and taking measurements.
Center punch - a round rod with a pointed working end in its conical part. Pointing angle 45 - 60°. The other (shock) end has a slightly convex surface. A center punch is made from tool steel and hardened. Serves for drawing recesses before drilling.
At present, small automatic (spring) center punches are used in the jewelry industry (Fig. 30). Being the most convenient and productive tool, they are increasingly replacing conventional center punches. The automatic center punch is designed for fast punching with a simple push on the top; the other hand is free from work. In the case of a mechanical center punch there are: a shock spring, a rod with a center punch and a striker. The impact force is regulated by a special device.

The plate for marking jewelry blanks is a flat steel (not hardened) sheet 150X150X2 mm. On each side there are concentric circles and their division by axes into 8, 10, 12, 14 parts. To center the workpiece, one of the axes must have a dividing scale. In this way, both marker plates, each of which has a two-sided marking, provide a quick and error-free division of the workpiece into almost any number of radial axes. The marking plate allows you to accurately find symmetrical points (outside the workpiece) for the support leg of the compass, perform mates, draw connecting arcs when marking a symmetrical pattern. To bond the plate to the workpiece, the surface of the plate must be rough.
Before marking, they carefully check whether the workpiece has defects, shells, cracks, captivity. After that, the workpiece is annealed with a soldering machine or in a muffle furnace, so that its surface is evenly oxidized - marking marks are more noticeable on a dark surface. In the middle of the front surface of the workpiece, a longitudinal axis is drawn along the ruler, which will serve as the marking base. Then the workpiece is placed on the marking plate so that the axis of the workpiece coincides with the axis of the plate having a dividing scale. This makes it possible to quickly determine the center of the markup. Having on the marking plate the risks of dividing the circles by the required number, they are easily found on the workpiece. Then, with the help of a compass, figures are constructed or the centers of other circles are found. The centers of the circles on the workpiece are kerned.
The marking process is based on the division of lines, the construction of some geometric shapes and the radial division of circles, which are either the ultimate goal of marking or the basis for marking complex patterns and placements. The construction of figures is done taking into account the observance of the markup center.
To divide a segment of the longitudinal axis in half with a perpendicular axis (Fig. 31) with a compass from the point BUT(the end of the longitudinal axis) with a radius somewhat greater than half the length of the segment, an arc is drawn. Then with the same radius from the point AT(the other end of the longitudinal axis) draw another arc and through the points of intersection of the arcs With and O draw a straight line, which will serve as a transverse axis and divide the longitudinal axis in half. Intersection point O will be the center of the markup. Further division of the straight line is carried out from the center with a compass solution of the required size, which is determined by the divisions of the caliper or scale bar.

A rhombus along the diagonal and side is built in the same way as dividing a straight line in half by a perpendicular axis. From a point BUT(Fig. 32) draw an arc with a radius equal to the side of the rhombus, and after drawing the same arc from the point AT received points With and D connect with dots BUT and AT.

To build a rhombus along two diagonals, the large diagonal is divided in half by a perpendicular axis (small diagonal), on which segments equal to half of the given small diagonal are laid off from the center of the intersection of the diagonals.
The construction of a square along the diagonal is carried out using a circle drawn from the center of the intersection of perpendicular axes with a radius equal to half the diagonal. The points of intersection of the axes with the circle are connected.
The construction of a square along the side is carried out as follows. From the center of the intersection of perpendicular axes O(Fig. 33) on the horizontal axis, a compass makes a notch with a radius equal to half of the given side. through the given point To draw a straight line perpendicular to the horizontal axis, on which segments are laid from point K KA and HF equal to half of the given side. through dots BUT and AT from the center of the markup O draw a circle and through the center of the circle O from points BUT and AT draw straight lines until they intersect the circle at points With and D. Received points BUT,AT, With and D connected in series. By connecting in series the vertices of the square with the points of intersection of the axes with the circle, an octagon is obtained.

To build an equilateral triangle (Fig. 34) from the intersection point of perpendicular axes O draw a circle. Then with a compass opening equal to the radius, from the point of intersection of the axis with the circle (say, O 1) make serifs on the circumference BUT and AT. Points obtained on the circle BUT and AT connected in series with a point With(point on circle opposite to point O 1).

A hexagon is built in a circle, which is divided into six parts by a radius. The points obtained on the circle are connected in series.
A dodecagon is constructed similarly to a hexagon, but the circle is divided into 12 parts.
The construction of a pentagon is done as follows. Circle radius OA(Fig. 35) is divided in half, and from the middle of it (points O 1) draw an arc with a radius OD until it intersects with the diameter AB at the point With. Distance between points With and D will be the side of the pentagon, and the segment OS will be equal to the side of the decagon. Dividing the circle with a compass opening equal to CD, get five serifs, which are sequentially connected to each other.

For a decagon, the circle is divided by a compass opening equal to OS.
When constructing a heptagon (Fig. 36), as in constructing a triangle, from point O, lay an arc with a compass opening equal to the radius, until it intersects with a circle. Intersection points BUT and AT connect, and cut AC(half straight AB) will be the side of the heptagon.

The pentagon (Fig. 37) is built like a heptagon until a segment is obtained AC. Then from points BUT and With compass solution equal to AC, make serifs until they intersect at a point D. Point D connected to the center of the circle O, and a point E obtained by crossing the line OD with a circle, connect with a point BUT. Line segment AE and will be the side of the nonagon.

The division of a circle into 3, 4, 5, 6, etc. equal parts is carried out in the same way as the construction of polygons inscribed in circles. The circle points found for the vertices of the polygons are connected to the center of the circle. When dividing a circle into an even number of equal parts, the axes will pass through the center of the circle, connecting two opposite points; when divided into an odd number of parts, rays are formed emanating from the center of the circle through points found on the circle.
To facilitate marking and if it is impossible to carry out complex constructions on the workpiece, the coefficients given in Table. 8. It has two columns. One indicates the number of parts into which you want to divide the circle, the other - the number by which you need to multiply the radius of the circle to get the size of the part.

Table 8

Coefficients for determining the size of parts of a circle

An oval with two axes of symmetry can be built along a given major axis (Fig. 38, a). To do this, a straight line equal to a given major axis is divided in half by two identical circles, the diameters of which are equal to half the straight line. Then, having found the centers on the continuation of the minor axis (perpendicular through the middle of the major axis), the circles are mated with arcs.

According to the given major and minor axes, the oval is constructed as follows (Fig. 38, b). Points are applied on perpendicular to the major and minor axes A, B, With and D, which define the specified dimensions of the axes. Then from the center of the intersection of the axes O radius R, equal to half the major axis, draw an arc AE connecting the major and minor axes. Distance CE on the continuation of the minor axis will be the difference between the major and minor semiaxes. On a straight line AC postpone cut CF, equal to CE, and the remaining line AF bisected by a perpendicular line. Perpendicular through the midpoint of a line AF, intersects the major axis at the point 1 and small at the point 2 . Points are found on the axes of the future oval 3 and 4 , symmetrical to the points 1 and 2 . The four points found will be the centers of the arcs that make up the oval. From points 1 and 3 draw arcs with a radius R 1 , and from the points 2 and 4 - arcs with a radius R 2 .
The construction of an oval along a given minor axis (Fig. 38, c) is carried out using a circle drawn from the intersection point of the axes O radius equal to the given minor axis. Points of intersection of the circle with the minor axis BUT and AT connected by straight lines to the points of intersection of the circle with the major axis O 1 , and O 2. Then, taking as the center of the point BUT and AT, with a radius equal to the diameter of the circle, arcs are drawn until they intersect with continuations of straight lines JSC 1 , AO 2 , IN 1 , VO 2 in points D, F, C, E. The resulting arcs are connected by arcs CD and EF from centers respectively O 1 , and O 2 .
An ellipse differs from an oval in that it always has two axes of symmetry. An ellipse is built along the given major and minor axes (Fig. 39). From the center of the intersection of the axes O two circles are drawn: one with a radius equal to the semi-major axis, the other with a radius equal to the minor semi-axis. Circles are divided by diameters into several equal parts (for example, 12). Vertical lines are drawn from the division points on the large circle, and horizontal lines from the division points on the small circle. The intersection points of these lines define the points of the ellipse. The more division points of the circles, the easier it is to build an ellipse.

When performing graphic work, you have to solve many construction tasks. The most common tasks in this case are the division of line segments, angles and circles into equal parts, the construction of various conjugations.

Dividing a circle into equal parts using a compass

Using the radius, it is easy to divide the circle into 3, 5, 6, 7, 8, 12 equal sections.

Division of a circle into four equal parts.

Dash-dotted center lines drawn perpendicular to one another divide the circle into four equal parts. Consistently connecting their ends, we get a regular quadrilateral(Fig. 1) .

Fig.1 Division of a circle into 4 equal parts.

Division of a circle into eight equal parts.

To divide a circle into eight equal parts, arcs equal to the fourth part of the circle are divided in half. To do this, from two points limiting a quarter of the arc, as from the centers of the radii of the circle, notches are made outside it. The resulting points are connected to the center of the circles and at their intersection with the line of the circle, points are obtained that divide the quarter sections in half, i.e., eight equal sections of the circle are obtained (Fig. 2 ).

Fig.2. Division of a circle into 8 equal parts.

Division of a circle into sixteen equal parts.

Dividing an arc equal to 1/8 into two equal parts with a compass, we will put serifs on the circle. Connecting all serifs with straight line segments, we get a regular hexagon.

Fig.3. Division of a circle into 16 equal parts.

Division of a circle into three equal parts.

To divide a circle of radius R into 3 equal parts, from the point of intersection of the center line with the circle (for example, from point A), an additional arc of radius R is described as from the center. Points 2 and 3 are obtained. Points 1, 2, 3 divide the circle into three equal parts.

Rice. 4. Division of a circle into 3 equal parts.

Division of a circle into six equal parts. The side of a regular hexagon inscribed in a circle is equal to the radius of the circle (Fig. 5.).

To divide a circle into six equal parts, it is necessary from points 1 and 4 intersection of the center line with the circle, make two serifs on the circle with a radius R equal to the radius of the circle. Connecting the obtained points with line segments, we get a regular hexagon.

Rice. 5. Dividing the circle into 6 equal parts

Division of a circle into twelve equal parts.

To divide a circle into twelve equal parts, it is necessary to divide the circle into four parts with mutually perpendicular diameters. Taking the points of intersection of the diameters with the circle BUT , AT, With, D beyond the centers, four arcs are drawn by the radius to the intersection with the circle. Received points 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 and points BUT , AT, With, D divide the circle into twelve equal parts (Fig. 6).

Rice. 6. Dividing the circle into 12 equal parts

Dividing a circle into five equal parts

From a point BUT draw an arc with the same radius as the radius of the circle before it intersects with the circle - we get a point AT. Lowering the perpendicular from this point - we get the point With.From point With- the midpoint of the radius of the circle, as from the center, by an arc of radius CD make a notch on the diameter, get a point E. Line segment DE equal to the length of the side of the inscribed regular pentagon. By making a radius DE serifs on the circle, we get the points of dividing the circle into five equal parts.

Rice. 7. Dividing the circle into 5 equal parts

Dividing a circle into ten equal parts

By dividing the circle into five equal parts, you can easily divide the circle into 10 equal parts. Having drawn straight lines from the resulting points through the center of the circle to the opposite sides of the circle, we get 5 more points.

Rice. 8. Dividing the circle into 10 equal parts

Dividing a circle into seven equal parts

To divide a circle of radius R into 7 equal parts, from the point of intersection of the center line with the circle (for example, from the point BUT) describe how from the center an additional arc the same radius R- get a point AT. Dropping a perpendicular from a point AT- get a point With.Line segment sun equal to the length of the side of the inscribed regular heptagon.

Rice. 9. Dividing the circle into 7 equal parts

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Division of a circle into equal parts. Drawing markup.

Example. It is required to divide a circle into 13 equal parts, the radius of which is 200 mm.

According to the table, the number corresponding to 13 divisions is 0.4786. Multiplying 0.4786 by 200 mm, we get: 0.4786X200 = 95.72 mm.

Setting aside the resulting distance on the marked circle with a compass, we divide it into 13 equal parts.

Table 22 Dividing a circle into equal parts

Drawing markup. Wrench marking (Fig. 80) must be performed in the following sequence:

1. Study the drawing.

2. Check the workpiece.

Rice. 80. Examples of marking (planar) wrench

3. Paint over the markings with vitriol or chalk, diluted to the density of milk.

4. Drive a bar into the mouth of the key,

5. Draw a center line along the key.

6. Draw a circle according to the drawing and divide it into six parts.

7. Repeat the same operations on the second key head.

8. Apply all dimensions according to the drawing.

Division of a circle into three equal parts. Install a square with angles of 30 and 60 ° with a large leg parallel to one of the center lines. Along the hypotenuse from a point 1 (first division) draw a chord (Fig. 2.11, a), getting the second division - point 2. Turning the square and drawing the second chord, get the third division - point 3 (Fig. 2.11, b). By connecting points 2 and 3; 3 and 1 straight lines form an equilateral triangle.

Rice. 2.11.

a, b - c using a square; in- using a circle

The same problem can be solved using a compass. By placing the support leg of the compass at the lower or upper end of the diameter (Fig. 2.11, in) describe an arc whose radius is equal to the radius of the circle. Get the first and second divisions. The third division is at the opposite end of the diameter.

Dividing a circle into six equal parts

The compass opening is set equal to the radius R circles. From the ends of one of the diameters of the circle (from the points 1, 4 ) describe arcs (Fig. 2.12, a, b). points 1, 2, 3, 4, 5, 6 divide the circle into six equal parts. By connecting them with straight lines, they get a regular hexagon (Fig. 2.12, b).

Rice. 2.12.

The same task can be performed using a ruler and a square with angles of 30 and 60 ° (Fig. 2.13). The hypotenuse of the square must pass through the center of the circle.

Rice. 2.13.

Dividing a circle into eight equal parts

points 1, 3, 5, 7 lie at the intersection of the center lines with the circle (Fig. 2.14). Four more points are found using a square with angles of 45 °. When receiving points 2, 4, 6, 8 the hypotenuse of a square passes through the center of the circle.

Rice. 2.14.

Dividing a circle into any number of equal parts

To divide a circle into any number of equal parts, use the coefficients given in Table. 2.1.

Length l chord, which is laid on a given circle, is determined by the formula l = dk, where l- chord length; d is the diameter of the given circle; k- coefficient determined from Table. 1.2.

Table 2.1

Coefficients for dividing circles

To divide a circle of a given diameter of 90 mm, for example, into 14 parts, proceed as follows.

In the first column of Table. 2.1 find the number of divisions P, those. 14. From the second column write out the coefficient k, corresponding to the number of divisions P. In this case, it is equal to 0.22252. The diameter of a given circle is multiplied by a factor and the length of the chord is obtained l=dk= 90 0.22252 = 0.22 mm. The resulting length of the chord is set aside with a measuring compass 14 times on a given circle.

Finding the center of the arc and determining the size of the radius

An arc of a circle is given, the center and radius of which are unknown.

To determine them, you need to draw two non-parallel chords (Fig. 2.15, a) and set up perpendiculars to the midpoints of the chords (Fig. 2.15, b). Centre O arc is at the intersection of these perpendiculars.

Rice. 2.15.

Pairings

When performing machine-building drawings, as well as when marking workpieces in production, it is often necessary to smoothly connect straight lines with arcs of circles or an arc of a circle with arcs of other circles, i.e. perform pairing.

Pairing called a smooth transition of a straight line into an arc of a circle or one arc into another.

To build mates, you need to know the value of the radius of the mates, find the centers from which the arcs are drawn, i.e. interface centers(Fig. 2.16). Then you need to find the points at which one line passes into another, i.e. connection points. When constructing a drawing, mating lines must be brought exactly to these points. The point of conjugation of the arc of a circle and the line lies on the perpendicular, lowered from the center of the arc to the conjugate line (Fig. 2.17, a), or on a line connecting the centers of mating arcs (Fig. 2.17, b). Therefore, to construct any conjugation by an arc of a given radius, you need to find interface center and point (points) conjugation.

Rice. 2.16.

Rice. 2.17.

The conjugation of two intersecting lines by an arc of a given radius. Given straight lines intersecting at right, acute and obtuse angles (Fig. 2.18, a). It is necessary to construct conjugations of these lines by an arc of a given radius R.

Rice. 2.18.

For all three cases, the following construction can be applied.

1. Find a point O- the center of the mate, which must lie at a distance R from the sides of the corner, i.e. at the point of intersection of lines passing parallel to the sides of the angle at a distance R from them (Fig. 2.18, b).

To draw straight lines parallel to the sides of an angle, from arbitrary points taken on straight lines, with a compass solution equal to R, make serifs and draw tangents to them (Fig. 2.18, b).

• 2. Find the junction points (Fig. 2.18, c). For this, from the point O drop perpendiculars to given lines.
• 3. From point O, as from the center, describe an arc of a given radius R between junction points (Fig. 2.18, c).